Looks pretty straight forward. My only real issue I see is how to get the new plumbing in place of the old plumbing with the bottom piece fixed in the ground and the vertical vent fixed as well. Is there a trick to this?

Okay you should have enough room at the bottom to cut the pipe below the sani-tee for the washer standpipe. Calculate where you want the utility sink drain to come in and make the cut. You can run a dogleg on the sink drain after the vent on the drain side...

Cut up above for the vent and if you don't have enough wiggle to connect using the socket on the vent sani-tee then use a banded coupling such as a Fernco Pro-Flex...

O.k. I was out of town all week so I didn't make any progress, but I did knock out the drain side plumbing this afternoon. I'll take care of the water side tomorrow and hook up the sink to make sure everything works and then I'll be back onto the drywall. Thanks for all the help. I'll post completed pictures.